Mathematics College

For the function below, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing
toxx ?
f(x)= 3%
X-X-112x - 4
(a) The critical number(s) is/are -
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
(b) on which intervals is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. Increasing on
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
OB. Never increasing
(c) On which intervals is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
ОО
A. Never decreasing
B. Decreasing on
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression, Vse a comma to senartowo

Answers

Answer 1

Step-by-step explanation:

We must do the first derivative test. Here is the steps:

Step 1: Differentiate the polynomial once

we get

[tex]2 {x}^{2} - 2x - 112[/tex]

Step 2: Set this equal to zero and solve for x.

[tex]2 {x}^{2} - 2x - 112 = 0[/tex]

[tex] {x}^{2} - x - 56 = 0[/tex]

[tex](x - 8)(x + 7) = 0[/tex]

[tex]x = 8[/tex]

[tex]x = - 7[/tex]

The solutions are your critical points.

So our critical points are (8,-7).

Step 3: Plot -7 and 8 on a number line. First, pick a number lesser than -7 and plug plug in the derivative function.

Let use -10.

[tex]( - 10 - 8)( - 10 + 7) = 54[/tex]

Since that number is positive, this means are increasing when (-oo,-7)

Next, pick a number greater than 8. Let use 9.

[tex](9 - 8)(9 + 7) = 16[/tex]

Since that is positive, the interval is increasing whe (8,oo)

C. If we pick a number in between -7 and 8, we will get a negative number which means the function is decreasing on interval (-7,8)

Related Questions

a formula one racecar driver estimates that he needs to maintain an average speed of 113 miles per hour in order to set a new lap record on an Australian racetrack. since australia uses si units, the average speed will be reported to the driver in kilometers per hour. if the driver successfully maintained an average speed of 113 miles per hour during the lap, what would the report show as his average speed in kilometers per hour? round your answer to the nearest hundredth

Answers

Answer:

181.82 km/h

Step-by-step explanation:

1 mile = 1.609 km

so 113 miles/hour = 113 * 1.609 = 181.82 km/h

Can someone please help me with this? I have a test tommorow on this subject and I'm very confused. :(

Prism: V = Bh
Cylinder: V = πr²h

Answers

Answer:

452.16 in. or 144π if the answer needs to be in terms of pi.

Step-by-step explanation:

In this case, all of the information is given to you. You can determine this is a cylinder because of its circular bases. Your height is given on the side as 9in. Your radius is given on the base as 4in. You can tell that this value is the radius and not the diameter because the line only covers half of the circular base. If the line went from one edge to the other, you would need to divide the given value by 2. From there, you can just plug the numbers into the proper equation.

V = πr²h

V = π(4)²(9)

V = 452.16 or 144π

The ratio of girls to boys in a class is 9:6. The average class size in the school is 25 students. Suppose this class is representative of all the students in the school. How many students in this class are boys?

Answers

Step-by-step explanation:

Here is the correct answer...

I hope you understand...

A shopkeeper buys a dress for $40
She sells it for $48
Work out the percentage increase in the price of the dress.

Answers

Answer:

48 - 40 = $8, there is a $8 dollar increase.

Formula for change of percentage;

changed price

___________ x 100% (100/100)

original amount

Replace those values with the values we found;

40/48 x 100/100 = 20% increase.

Find the measure of the angle. (two more and i'm done, sorry)

Answers

Answer:

c=102°

b=(360-204)/2 = 78°

Answers:

b = 78

c = 102

=================================

Explanation:

Let's find angle b. This angle adds to the 102 to get 180 since the two angles form a straight angle.

102+b = 180

b = 180-102

b = 78

Then we can apply the same idea to find angle c

b+c = 180

78+c = 180

c = 180-78

c = 102

A shortcut to find angle c is to recall that vertical angles are congruent. The proof of the vertical angle theorem is effectively the steps shown above.

2
Type the correct answer in the box. Use numerals instead of words.
What is the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet?
The total surface area is about
square feet.

107
110
132
93

Answers

The area of the equilateral triangular pyramid is the amount of space on it

The total surface area is 107 square feet

How to determine the total surface area?

The given parameters are:

Base (b) = 6 feet

Slant height (l) = 10 feet

The lateral surface area is calculated using:

L = 1.5bl

So, we have:

L = 1.5 * 6 * 10

Evaluate the product

L = 90

The total surface area is calculated using:

T = L + 0.25√3b^2

So, we have:

T = 90 + 0.25√3 * 6^2

Evaluate

T = 107

Hence, the total surface area is 107 square feet

Answers

Answer:

50 states bb bbdbeu28nefd

20 States Primary enforcement laws for all occupants: 20 states—Alaska, California, Delaware, Hawaii, Illinois, Indiana, Kentucky, Louisiana, Maine, Minnesota, Mississippi, New Mexico, New York, Oregon, Rhode Island, South Carolina, Texas, Utah, Washington and Wisconsin, plus the District of Columbia, Guam, the Northern Mariana

Show all steps necessary to verify the trigonometric identity:
1 - 2cos^2x = 2sin^2x - 1

Answers

Step-by-step explanation:

please mark me as brainlest

Using trigonometric identity sin²θ+cos²θ=1, the given identity is proved.

The given trigonometric identity is 1-2cos²x = 2sin²x-1.

What are trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.

Using trigonometric identity sin²θ+cos²θ=1

Here, 1-2cos²x = 2sin²x-1

⇒ 1+1=2sin²x+2cos²x

⇒ 2=2(sin²x+cos²x)

⇒ 2=2(1)

⇒ 2=2

LHS=RHS

Therefore, using trigonometric identity sin²θ+cos²θ=1, the given identity is proved.

Learn more about the trigonometric identity here:

https://brainly.com/question/24377281.

#SPJ2

Follow the steps to solve the equation using algebra tiles. -4x + 1 = x + (-4)

Answers

Answer:

x=1

Step-by-step explanation:

This can be simplified to -4x+1=x-4

add 4 to both sides

-4x+5=x

Flip it so it is easier to work with

x=-4x+5

add 4x to both sides

5x=5

Divide by 5

x=1

Write 24:18 in a simplest form

Answers

We can start by the simplest factor. Which is 2.
24:18 will be divided by 2 both sides.That will be 12:9.
We then realize that 12 and 9 are both multiples of 3.
So we take 12:9 divided by 3 on both sides again.Which would be 4:3.
The factors end here which will give us 4:3 as the simplest form.
Hope this helps !!

Answer:

4:3

Step-by-step explanation:

24:18

Divide each side by 6

24/6 : 18/6

4:3

Please help asap! I will gave brainlest!

Answers

Answer:

0,180

Step-by-step explanation:

[tex]8 \tan(x) = 0[/tex]

[tex] \tan(x) = 0[/tex]

[tex]x = 0 + 180n[/tex]

This means 0, 180 are the solutions.

0’180 that’s

Will be the answer

Select multiples of 4. You will select three.

2
4
22
36
42
48

Answers

Answer:

Multiples of 4 are the following:

43648

Step-by-step explanation:

2 is a factor of 4, not a multiple. The rest of the numbers listed are multiples of 2. But only the 3 listed above are multiples of 4.

Answer:

4,36,48

Step-by-step explanation:

The multiples of 4 is: 36,48,and 4 because there all in the multiplication chart.
*Please give brainliest*

The pH scale measures the acidity of a liquid as a function of its hydrogen ion(H+) concentration pH=-log[H+] A chemist needs to prepare a solution with a pH of three. What H+ concentration should the solution have?

Answers

Answer:

H+ = 0.001

Step-by-step explanation:

3 = -log[H+]

Identity to use: [tex]-log_{b}(a) = log_{b}(1/a)[/tex]

3 = log[ 1 / H+ ]

Identity to use: [tex]10^{log(x)} = x[/tex]

Therefore, I am going raise each side of the equation to the power of 10 to isolate [ 1 / H+ ]

10³ = [tex]10^{log(\frac{1}{H+} )}[/tex]

1000 = 1 / H+

H+ = 1 / 1000

Answer: H+ = 0.001

Using the cross multiplication method, which of the following is the solution to 1/(x+1) = 17/(x+2)?

Answers

Answer:

x = -15/16

Step-by-step explanation:

see image.

Cross-multiply and combine like terms. Finally divide to get x all by itself.

see image.

Someone good at math pls help me will give brainlist and the most life saver in the world

Answers

Answer:

The answer is -46,8

ok so!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! mark me brainliest

Find dy/dx in terms of x and y

3x sin y + 2 cos y = sin x

Answers

[tex]3x\sin y+2\cos y=\sin x[/tex]

[tex]\dfrac{\mathrm d(3x\sin y+2\cos y)}{\mathrm dx}=\dfrac{\mathrm d(\sin x)}{\mathrm dx}[/tex]

[tex]\dfrac{\mathrm d(3x)}{\mathrm dx}\sin y+3x\dfrac{\mathrm d(\sin y)}{\mathrm dx}+\dfrac{\mathrm d(2\cos y)}{\mathrm dx}=\cos x[/tex]

[tex]3\sin y+3x\cos y\dfrac{\mathrm dy}{\mathrm dx}-2\sin y\dfrac{\mathrm dy}{\mathrm dx}=\cos x[/tex]

Solve for dy/dx :

[tex]3\sin y+\left(3x\cos y-2\sin y\right)\dfrac{\mathrm dy}{\mathrm dx}=\cos x[/tex]

[tex]\left(3x\cos y-2\sin y\right)\dfrac{\mathrm dy}{\mathrm dx}=\cos x-3\sin y[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\boxed{\dfrac{\cos x-3\sin y}{3x\cos y-2\sin y}}[/tex]

A cone-shaped frozen yogurt cup has a radius of 5 cm and a height of
9 cm. How many cubic centimeters of frozen yogurt can the cup hold?
Approximate your answer to the nearest hundredth.

Answers

Answer:

235.62 Cubic centimeters

Step-by-step explanation:

[tex]v = \frac{1}{3}\pi \: r {}^{2} h \: = \frac{1}{3} \times \pi \times 5 {}^{2} \times 9 \\ \\ = 75\pi = 235.62[/tex]

Answer:

235.62 Cubic centimeters

Step-by-step explanation:

have a nice day.

What is 17/5 as a mixed number in simplest form ?

Answers

Answer:

3 [tex]\frac{2}{5}[/tex]

Answer:

3 and 2/5 i believe

please say if im wrong or right

Step-by-step explanation:

How much will a person pay for 7 pounds of bananas at a price of $0.49 per pound?
<

Answers

Answer:

$3.43

Step-by-step explanation:

Multiply 7 by 0.49

WORTH 100 POINTS WILL PICK BRAINLYLIST Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each prism with its volume or dimensions.

Answers

Answer:

1, 1/2, 3/2

Step-by-step explanation:

This is a prism (a 3d rectangle) and so your formula for finding the volume is V= L x W x H.

For the prism:

L= 1 (4 cubes x 1/4 = 4)

W = 1/2 (2 cubes x 1/4 = 1/2)

H = 3/2 (6 cubes x 1/4 = 6/4 = 3/2)

That's your answer, the tile 1, 1/2, 3/2

Matthew's family traveled 3/8 of the distance to his grandmother’s house on Saturday. They traveled 3/5 of the remaining distance on Sunday. What fraction of the total distance to his grandmother’s house was traveled on Sunday?

Answers

Answer:

3/8 of the total distance.

Step-by-step explanation:

After Saturday = 8/8 - 3/8 = 5/8 of distance left.

Sunday = 5/8 x 3/5 = 3/8 distance.

Hope this helps!

A restaurant manager bought a case of 12 bottles of water. He paid 90p per bottle. He sold 1/4 of the bottles for £2.10 per bottle and the rest of the case for £2.40 per bottle. a) How much profit did he make? b) Write the profit as a percentage.

Answers

Step-by-step explanation:

12 bottles for 0.90 per bottle = 12×0.90 = £10.80 as initial cost.

1/4 of 12 = 12×1/4 = 12/4 = 3 bottles

so, 3 bottles are sold for £2.10 per bottle = 3×2.1 = £6.30

the rest (12-3) 9 bottles are sold for £2.40 per bottle = 9×2.4 = £21.60

so, the total sales was 6.3 + 21.6 = £27.90.

the profit is then sales minus initial cost :

27.9 - 10.8 = £17.10

1% of the initial cost is 10.8/100 = 0.108

how often does 1% fit into the total profit ?

17.1/(10.8/100) = 17.1×100/10.8 = 158.3333333...%

so, the profit is 158.3333333...% of the initial cost.

A news article reports that 52% of voters plan to vote for Vicente and 48% of voters plan to vote for Raul.

The margin of error is 3%.

Is there enough statistical evidence to say that Vicente is in the lead?

Answers

No, because the confidence interval do not overlap we do not have enough evidence to say that the parameters are different.

Confidence interval of the data

The confidence interval will help to determine if there is enough evidence in the statistical data draw conclusion that Vicente has the lead.

The confidence interval is 48% - 3% to 48% + 3%, which is equivalent to 45% to 51%.

Since 52% does not lie in the above interval, therefore we can say no, because the confidence interval do not overlap we do not have enough evidence to say that the parameters are different.

Learn more about confidence interval here: https://brainly.com/question/15712887

Answer:

Step-by-step explanation:

Hellllllllllpppppppp

Answers

Answer:

Step-by-step explanation:

Translate up & left then reflect over y axis.

Answer:

Step-by-step explanation:

First you have to translate up and then left, then reflect over the y axis.

The graph of a proportional relationship contains the point (8, 4).

What is the corresponding equation?

y=−2/1x

y=−1/2x

y=1/2x

y=2/1x
Please Help

Answers

Answer:

y = 1/2x

Step-by-step explanation:

Points are (8,4)

x = 8

x = 8y = 4

y= −2/1x

4= -2(8)

4= -16

That's wrong

y= −1/2x

4= -1/2(8)

4= -4

That's wrong

y=1/2x

4=1/2(8)

4=4

That's right

y=2/1x

4=2(8)

4=16

That's wrong

So the answer is choice C

3x-8=3(x-3)-2
Is there a answer to this problem? I cant find one

Answers

Answer:

The input is a contradiction: it has no solutions

Is this a good app for school
what is 122x1,2222

Answers

Answer:

122x12222 = 1491084

Answer:

It is a good app, when used the right way.

Step-by-step explanation:

Your question isn't properly described. 122x1,2222, is that 1.2222 or was it supposed to be 12,222?

Name the relationship between ∠a and ∠b.

Answers

Answer:

B. Adjacent

Step-by-step explanation:

Supplementary angles add up to 180 degrees, so cross of A. Vertical angles are directly across from each other, so cross off C. Corresponding angles are related to lines and a transversal which you don't have, so you can cross of D, leaving the answer as B.

Hopefully this helps - let me know if you have any questions!

How do I solve for y ?

Answers

Answer: 52

Step-by-step explanation:

.
evaluate 16^-3/4
Evaluation of the exponents

Answers

Answer:

I think it is -12

Multiply -0.75 (3 quarters) by 16.

The negative cancels out the positive number.

Since the exponent is not saying multiply the number by itself a number of times, we could make a hypothesis that this is just multiplication.

Normally, this ↑ is not the case, but here, I could make an exception.

I hope this helps you, let me know if you need something else.

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